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Original Articles

A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with Applications

, &
Pages 2309-2342 | Received 05 Aug 2010, Published online: 09 Jul 2012
 

Abstract

In this article, we give a new simultaneous decomposition concerning the general matrix quaternity over an arbitrary division ring ℱ. A practical algorithm for the decomposition of the matrix quaternity is also presented. As applications, we establish some necessary and sufficient conditions for the existence of the general solutions to the systems of matrix equations

and
over ℱ. In addition, we give the expressions of the general solutions to the systems when the solvability conditions are satisfied. Numerical examples are also given to illustrate the results of this article. Moreover, we mention that the findings of this article extend the some known results in the literature.

2000 Mathematics Subject Classification:

ACKNOWLEDGMENTS

This research was supported by the grants from the Ph.D. Programs Foundation of Ministry of Education of China (20093108110001), the Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (09YZ13), Natural Science Foundation of China (60672160, 11171205), Singapore MoE Tier 1 Research Grant RG60/07, and Shanghai Leading Academic Discipline Project (J50101).

The authors would like to thank a referee very much for his or her valuable suggestions and comments, which resulted in a great improvement of the original manuscript.

Notes

Communicated by J.-T. Yu.

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